Related papers: Generalized statistics in one dimension
In this note, we provide a unifying framework to investigate the computational complexity of classical spin models and give the full classification on spin models in terms of system dimensions, randomness, external magnetic fields and types…
A formulation of quantum mechanics, which begins by postulating assertions for individual physical systems, is given. The statistical predictions of quantum mechanics for infinite ensembles are then derived from its assertions for…
After a short discussion of the intimate relation between the generalized statistics and supersymmetry, we review the recent results on the nonlinear supersymmetry obtained in the context of the quantum anomaly problem and of the universal…
Some methods for the determination and the most precise values of constants of an extended Standard Model, which include the gravitation interaction and massive neutrinos, are presented. Accuracies of constants at different energy scales…
We show that, in spite of a rather common opinion, quantum mechanics can be represented as an approximation of classical statistical mechanics. The approximation under consideration is based on the ordinary Taylor expansion of physical…
We introduce several statistics on ordered partitions of sets, that is, set partitions where the blocks are permuted arbitrarily. The distribution of these statistics is closely related to the q-Stirling numbers of the second kind. Some of…
Both statistics and quantum theory deal with prediction using probability. We will show that there can be established a connection between these two areas. This will at the same time suggest a new, less formalistic way of looking upon basic…
The typicality approach and the Hilbert space averaging method as its technical manifestation are important concepts of quantum statistical mechanics. Extensively used for expectation values we extend them in this paper to transition…
In a series of two papers we investigate the universal spectral statistics of chaotic quantum systems in the ten known symmetry classes of quantum mechanics. In this first paper we focus on the construction of appropriate ensembles of star…
Since the problem: "What is statistics?" is most fundamental in sceince, in order to solve this problem, there is every reason to believe that we have to start from the proposal of a worldview. Recently we proposed measurement theory (i.e.,…
We study exclusion statistics within the second quantized approach. We consider operator algebras with positive definite Fock space and restrict them in a such a way that certain state vectors in Fock space are forbidden ab initio.We…
We give a detailed account of the one-way quantum computer, a scheme of quantum computation that consists entirely of one-qubit measurements on a particular class of entangled states, the cluster states. We prove its universality, describe…
General non-commutative supersymmetric quantum mechanics models in two and three dimensions are constructed and some two and three dimensional examples are explicitly studied. The structure of the theory studied suggest other possible…
We discuss several algorithms for sampling from unnormalized probability distributions in statistical physics, but using the language of statistics and machine learning. We provide a self-contained introduction to some key ideas and…
In this paper I introduce quantile spectral densities that summarize the cyclical behavior of time series across their whole distribution by analyzing periodicities in quantile crossings. This approach can capture systematic changes in the…
We present a random matrix model suitable for the quantum mechanical description of a particle confined to move inside a two-dimensional domain. Here, the ensemble average corresponds to an average over domain shapes. Although this approach…
The random matrix ensembles (RME) of quantum statistical Hamiltonian operators, {\em e.g.} Gaussian random matrix ensembles (GRME) and Ginibre random matrix ensembles (Ginibre RME), are applied to following quantum statistical systems:…
Quantiles are very important statistics information used to describe the distribution of datasets. Given the quantiles of a dataset, we can easily know the distribution of the dataset, which is a fundamental problem in data analysis.…
Interpretations of quantum measurement theory have been plagued by two questions, one concerning the role of observer consciousness and the other the entanglement phenomenon arising from the superposition of quantum states. We emphasize…
The framework of generalized probabilistic theories is a powerful tool for studying the foundations of quantum physics. It provides the basis for a variety of recent findings that significantly improve our understanding of the rich physical…